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Materials Research Letters

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Strength and plasticity of nanolaminatedmaterials

Jian Wang, Qing Zhou, Shuai Shao & Amit Misra

To cite this article: Jian Wang, Qing Zhou, Shuai Shao & Amit Misra (2017) Strengthand plasticity of nanolaminated materials, Materials Research Letters, 5:1, 1-19, DOI:10.1080/21663831.2016.1225321

To link to this article: http://dx.doi.org/10.1080/21663831.2016.1225321

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MATER. RES. LETT., 2017VOL. 5, NO. 1, 1–19http://dx.doi.org/10.1080/21663831.2016.1225321

Strength and plasticity of nanolaminated materials

Jian Wanga , Qing Zhoua,b, Shuai Shaoc and Amit Misrad

aMechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA; bMaterials Science and Engineering, Xi’an JiaotongUniversity, Xi’an, Shaanxi, People’s Republic of China; cMechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA, USA;dDepartment of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

ABSTRACTThe mechanical behavior of nanolaminates is dominated by interfaces that act as sources, barriers,andpreferred sites for storage anddynamic recovery of glidedislocations. In this article, thedeforma-tionmechanisms of a variety of metal-based nanolaminates are reviewedwith emphasis on unusualmechanical properties such as ultra-high flow strength without loss of plastic deformability.

IMPACT STATEMENTThis paper reviews the current understanding of the mechanisms and mechanics of nanolaminatedcomposites, and discusses the future direction in predicting the mechanical behavior of laminatedcomposites.

ARTICLE HISTORYReceived 14 July 2016Accepted 13 August 2016

KEYWORDSNanolaminate; strength;plasticity; dislocations;interfaces

1. Introduction

Future energy, transportation, and defense technologiesdemand novel materials that tolerate extremes in tem-perature, stress, strain rate, and radiation to an extentthat far exceeds the limits of the most advanced materi-als to date. Nanolaminated materials have been demon-strated as promising to meet these needs due to theirunusual mechanical, electrical, and magnetic properties,and radiation damage tolerance [1–9].

Nanolaminated materials can be processed in theform of thin films via bottom-up processes such asphysical vapor deposition (PVD) [10,11] and electrode-position [12], or in the form of bulk materials viatop-down processes such as solid-state phase trans-

CONTACT Jian Wang jianwang@unl.edu Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE68588, USA

formation [13,14], accumulative roll bonding (ARB)[15,16], or solidification [13,17,18]. In epitaxial films,solid-state phase transformation, or eutectic solidifi-cation, energetically favorable crystallographic orienta-tion relationships and interface habit planes developnaturally during synthesis [10,11,14,18]. On the otherhand, ARB techniques not only lead to mechani-cally driven interfaces in order to maintain the com-patibility of plastic deformation between the adjacentlayers, but can also result in preferred orientation rela-tionships [15]. For example, in Cu–Nb, the interfacehabit planes are {111}Cu||{110}Nb for PVD [3,19–21]and {112}Cu||{112}Nb for ARB [15,21], both with thesame Kurdjumov–Sachs (KS) orientation relationship[5,22–27].

© 2016 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited.

2 J. WANG ET AL.

Unlike traditional materials, nanolaminated struc-tures contain a high density of interfaces that give rise tounprecedented properties [3–9,13,22,26–31]. Interfacesplay multiple roles in determining mechanical prop-erties: sources for nucleating plastic deformation car-riers (dislocations, phase transformation bands, twins,and shear bands), barriers for impeding the propaga-tion of these carriers, and preferred sites for storage,reassembly, and reaction (that may lead to recovery)of interface defects. With the ‘right’ characteristics,interfaces can possess significantly enhanced abilitiesto absorb and eliminate defects, granting the com-posite a highly effective healing mechanism and anunparalleled ability to mitigate damage accumulationinduced under severe loading conditions and/or envi-ronments. For instance, Cu–Nb-laminated compositeswith nanometer-scale layers exhibit outstanding ther-mal stability [22–24], ultra-high strength and plas-tic deformability [3,8,18,19,23,32,33], shock resistance[31,34], and high resistance to ion-irradiation-induceddamage [26,35]. A fundamental understanding of inter-faces and interface-dominated deformation events is,therefore, critical.

In this article, we review mechanisms of deformationand strengthening of metal–metal, metal–ceramics, andmetal–amorphous nanolaminated materials.

2. Strengtheningmechanisms

The flow strength of materials corresponds to the stressrequired, at a given strain rate, for continuous nucleation,multiplication, and propagation of plastic deformationcarriers, such as dislocations and twins in crystallinematerials and shear transformation zones (STZs) inamorphous materials. Strengthening of laminated mate-rials can be realized through tailoring layer thickness,

layer crystallography, a combination of constituentphases, and structure and properties of interfaces.

2.1. Layer thickness

Layer thickness is a microstructural parameter in deter-mining the mechanical properties of laminated compos-ites because the predominant deformation mechanismin a laminate changes with decreasing thickness of theconstituent layers [3,36]. Assuming that a certain inter-face acts as a barrier for the continuous motion of lat-tice dislocations, the development of plastic deformationrequires high local stresses that act on the dislocationto overcome the barrier. Corresponding to this theoreti-cal assumption, the dislocation pile-up-basedHall–Petchscaling law [8,37–43],σu ∝h−1/2 (σu is the flow strengthand h is the layer thickness), is applicable at h greater than∼100 nm, varying with the properties of constituentphases (Figure 1(a)). For h in the range of approxi-mately ∼10 to ∼100 nm, dislocation pile-up on thesame plane is unlikely due to the strong repulsion amonglike-sign coplanar dislocations. The dominant deforma-tion mechanism is confined layer slip (CLS) [25,44–49]that involves the propagation of single dislocation loopsparallel to the interfaces within layers (Figure 1(b)). Ath less than approximately 10 nm, experimental data on avariety of metallic nanolaminates indicate that the hard-ness or strength of laminated materials [3,8,36,45] showsno significant increase in the flow strength with decreas-ing h. This behavior has been interpreted as a change indominant deformation mechanism from CLS to inter-face crossing of single dislocations (Figure 1(c)). Theinterface barrier strength to the transmission of a sin-gle glide dislocation, without the mechanical advantageof a dislocation pile-up, is largely dependent on interfacestructures and properties, while being independent of the

Figure 1. Predominant deformation mechanisms in laminated A/B composites: dislocation pile-up, confined layer slip, and interfacecrossing, with respect to layer thickness. Arrows indicate the motion direction of dislocations.

MATER. RES. LETT. 3

layer thickness, but may drop when the layer thickness ison the order of dislocation core dimension [27,29,50–58].

2.2. Crystallography of the layers

The crystallography of the layers defines the geometricrelations of slip systems (slip planes and slip vectors) inthe adjacent layers with respect to the interface plane.The transmissibility of slip across an interface is relatedto the degree of continuity of slip planes and slip vec-tors across the interface. It is widely accepted that theoccurrence of slip transmission is geometrically favoredwhen a slip system of a crystal on one side of the inter-face is well-aligned with a slip system of the adjacentcrystal. Thus, a geometric factor can be introduced todescribe the extent of the slip continuity. If we let κ bethe minimum angle between their Burgers vector and θ

the minimum angle between the traces that the slip planemakes with the interface (Figure 2(a)), then an efficienttransmission pathway would be defined as the value of

χ = cos(

π

2θ

θc

)cos

(π

2κ

κc

), (1)

equal to or close to unity, where the angles θ c and κcare the limiting angles for κ and θ , respectively[59]. Theangle θ c is reasonably estimated to be ∼15 degrees cor-responding to the bow-out of a 1∼2 nm long disloca-tion segment which is pinned by the neighboring glideplanes. The angles κc may be larger, approximately 60degrees. This leads to transferring most components ofthe Burgers vector of the incoming dislocation into theadjacent layer. According to Equation (1), when either κ

or θ exceeds their corresponding thresholds, direct trans-mission is not possible unless the incoming dislocationline climbs in the interface to be parallel to the trace ofthe slip plane in the adjacent crystal. In addition, sliptransmissibility is also dependent on stresses and energybarriers associated with the transmission of a dislocationacross the interface. The Schmid factor of the outgo-ing slip system mout that determines the glide directionleads to a modification of Equation (1) to χσ = χmout .The difference in slip vectors of the paired slip systemsassociated with the transmission would lead to transmis-sion anisotropy between two layers because of the energypenalty associated with the residual dislocation at theinterface after slip transmission.

For laminates that share the same crystal structure andthe same crystallographic orientation, the slip planes andslip vectors are nearly continuous across the interfaces(Figure 2(b)), that is, κ = 0 and θ = 0. Thus χ = 1. Forexample of Cu/Ni and Cu/Ag systems that hold the cube-on-cube orientation relation [17,18,30,39,51,60–62], asmall change in the magnitude of the slip vector at

the interface poses a very minor resistance (or energypenalty) to slip, relative to the strength levels achievablein these materials. The strengthening effect in such kindof materials is thus ascribed to coherency stresses asso-ciated with the coherent interface as in Cu–Ni [29,50].However, Cu–Ag does not have coherency stresses dueto large lattice misfit and the slip transmission barrier isderived from the grid of misfit dislocations at the inter-face. When the two crystals hold the twin orientationrelation, for example, eutectic Cu/Ag laminated compos-ites with the twin orientation [63–65] or nanotwinnedmetals[66–72], the slip planes and slip vectors are of themirror symmetry across the interface (Figure 2(c)), thatis, κ > κc and θ = 0. Thus χ = 0. In addition, resolvedshear stresses on both slip systems have mirror sym-metry across the interface under a given applied stress;slip transmission is thus suppressed because of the nega-tive mout associated with the outgoing slip system. Highstrength in these materials is thus attributed to the dis-continuity of the slip system.

For laminates that are composed of dissimilar crys-tal structures, the discontinuity of slip systems intrin-sically exists in terms of slip planes and slip vectors.For example, in the Cu/Nb system, the large differencein the slip vectors (associated with a full dislocation inNb and a partial dislocation in Cu) favors slip trans-mission from Nb to Cu, while opposing slip transmis-sion from Cu to Nb [27,53]. Correspondingly, the flowstrength is determined with respect to slip transmis-sion from Cu to Nb. In addition, the crystallographicorientation influences the active slip systems within theindividual nanolayers. For example, in bcc/hcp systems(Mg/Nb nanolaminates), the {0001}Mg||{110}Nb inter-face is thermodynamically favored [73–75]. The primaryslip system {0001}<1120> (referred to as basal slip) ina hexagonal close-packed (hcp) structure is suppressedbecause of the zero Schmid factor when the laminate issubjected to loading normal to the interface. Non-basalslip systems with higher critical resolved shear stresses(CRSSs) compared to basal slip thus accommodate plas-tic deformation in Mg nanolayers [76–80]. Correspond-ingly, the Mg/Nb nanolaminates show unusually highflow strength, about five times higher than bulk Mg [73].

2.3. Combination of constituent phases

Anappropriate combination of constituent phases enablesthe optimization of strength and ductility of laminatedmaterials. According to plastic deformation mechanismsof constituent phases, laminated materials can be cate-gorized into three groups (Figure 3). Both constituentphases in groups 1 and 2 are crystalline and plasticallydeform via nucleation and propagation of dislocations.

4 J. WANG ET AL.

Figure 2. The crystallographyof slip across interface: (a) general case, (b) parallel slip systems case, and (c) twin-oriented case. The arrowsindicate the glide direction of lattice dislocations under compression normal to the interface.

Figure 3. Maximum strength of nanolaminated materials with respect to the combination of constituent phases: (a) metal–metal crys-talline laminates (b) metal-crystalline hard phase laminates, and (c) metal-metallic glass laminates. Black squares indicate the strengthof constituent 1 under the black line and red circles represent the strength of constituent 2 above the black line in the horizontal axis.Blue triangles represent the strength of nanolaminated composites.

For group 1, the CRSS for slip in both phases is sim-ilar (e.g. metal–metal nanolaminates). But for group 2,the CRSS in one constituent phase is much higher thanthat in the other, for example, metal-hard phase where‘hard phase’ is crystalline ceramic or intermetallic. Unlikegroups 1 and 2, group 3 is composed of one crystallinephase that plastically deforms via dislocations, and theother amorphous phase wherein STZs or shear bandsaccommodate plastic deformation.

Figure 3 shows the maximum strengths of laminatedcomposites with respect to the combination of con-stituent phases. For comparison, the maximum strengthof each constituent phase refers to the strength of the bulksingle crystal form. The strength of group 1 nanolami-nates is higher than that of each constituent counterpart,(2) Group 2 nanolaminates have strengths in between

the strengths of the two constituent counterparts, and (3)Group 3 nanolaminates can reach the yield strength of asingle amorphous phase.

The unusually high strength achieved for group 1nanolaminates can be accounted for based on threestrengthening mechanisms with respect to three types ofinterfaces. Type 1 interface is fully coherent and gener-ally occurs in very fine layers. Coherency stresses result-ing from lattice mismatch must be overcome in orderto achieve slip transmission [29,52,81]. Type 2 interfaceis twin interface that causes crystallographic disconti-nuity of the slip system, for example, corresponding tothe twin orientation strengthening mechanism [63–72].Type 3 interface is semi-coherent that has a low shearresistance in general, corresponding to weak shear inter-face strengtheningmechanisms [27,28,50,53,54,57,82]. It

MATER. RES. LETT. 5

Figure 4. Stress fields in 10 nmAl—5 nmTiN in associationwith the deposited interface dislocationswith the average spacing of 10 nm,showing (a) the normal stress parallel to the interface and (b) the resolved shear stress with respect to a glide plane (denoted as dashedwhite lines) [83].

is worth pointing out that a general rule of mixturesin terms of materials strength breaks down in thesenanolaminates.

In group 2 and 3 nanolaminated materials, the softmetal phases are strengthened, while the hard phasesare softened. This can be accounted for by disloca-tion–interface interactions. In order to maintain the geo-metric compatibility of a laminated microstructure dur-ing straining, the elastic and plastic deformation in lay-ers can be rationalized as follows. When a laminate issubjected to normal compression, plastic deformationfirst commences in softer layers and more plastic defor-mation develops in softer layers because of the loweryield strength and higher mobility of dislocations in thesoft phase compared to the hard phase. Dislocationsglide in the layers confined by the bounded interfaces,and deposit interface dislocations at the interfaces. Thedeposited dislocation arrays at interfaces produce resid-ual stresses: tensile (σxx(ρ)) in harder layers and com-pressive (−σxx(ρ)) in softer layers (Figure 4(a)) [83].Both increase with the increase in the density (ρ) ofthe accumulated interface dislocations. The density ρ

increases as the total deformation increases. Continuousdeformation requires an increase in the applied load-ing in order to overcome the residual compressive stressin the softer layer, resulting in strain hardening of thesofter phase. While the residual tensile stress in harderphases and the interaction force between these depositeddislocations at the adjacent interfaces produce a posi-tive resolved shear stress (Figure 4(b)), these reduce therequired applied stress for activating dislocations in theharder layers. Due to plastic co-deformability, the group2 nanolaminates exhibit high strength and plasticity.

For group 3 crystal-amorphous nanolaminated com-posites, plastic deformation in amorphous layers

(specifically in metallic glasses) is mainly carried outby STZs at small strains and shear banding at largestrains [84–89]. The deposited dislocations activate STZsin amorphous layers, and further deformation increasesthe density of STZs, resulting in shear banding inamorphous layers. Since the metal–amorphous inter-faces are less ordered, the incoming lattice disloca-tions are smeared along the interface, reducing the localstrain/stress concentration [82,90–96]. The maximumstrength thatmetal–amorphous nanolaminates can reachis mainly determined by the yield strength of the singleamorphous phase [97–100], although the nanolaminatecomposites exhibit plasticity.

2.4. Structures and properties of interfaces

Interfaces play triple roles in plastic deformation: sourcesfor nucleating dislocations, barriers for impeding themotion of dislocations, and platforms for dislocationreactions. In group 1 laminated composites, interfacesplay an obvious strengthening role: the strength of thecomposites is higher than that of each constituent phase.In group 2 and 3 laminated materials, the constraintfrom the layered geometry leads to induced plasticityin the hard phase facilitated by accumulated interfacedislocations.

The difficulty of dislocation transmission through aninterface is ascribed to differentmechanismswith respectto interface types. For coherent interface, coherencystresses play a crucial role in defining the maximumstrength that can be achieved (Figure 5(a)). The strengthmodel suggested by Hoagland et al. [29] is based onthe idea that a dislocation cannot traverse the compos-ite unless the net forces on the dislocation in all layersare the same sign. Thus, a stress must be applied that

6 J. WANG ET AL.

Figure 5. Schematic of key strengthening mechanisms in nanolaminates: (a) coherency stresses associated with lattice-matchednanolayers, (b) discontinuity of slip across twin interface, (c) glide dislocations pinned by grid of misfit dislocations at a semi-coherentinterface, and (d) cross-slip of lattice dislocation in the weak shear interface.

at least cancels the coherency stress in one of the twoconstituents. In systems such as Cu–Ni with equal layerthickness, the calculated coherency stresses are on theorder of 2GPa, comparable to the experimentally mea-sured strengths [8,28,60]. For twin boundary in single-phase or bi-phase metals [63–72], the change in crystalorientations between matrix and twinned crystals [101]results in the discontinuity of slip systems across twinboundaries (Figure 5(b)) [102,103]. Consequently, a highresolved shear stress is required to transmit a single dis-location across twin interfaces, thereby increasing thestrength [67,68,104–110].

A semi-coherent interface is composed of patches ofatomic coordination separated by misfit dislocations thatrelax the long-range coherency stresses. The arrays ofmisfit dislocations at interfaces must be cut (Figure 5c)for a single dislocation transmission across the inter-face [30,55]. Because of the intrinsic discontinuity ofslip across a semi-coherent interface, slip transmissionnaturally involves a re-nucleation process, as demon-strated in Cu–Nbmultilayers using atomistic simulations[27,28,111]. More importantly for a semi-coherent inter-face, interfaces show lower shear resistance than the the-oretical estimates of shear strengths on glide planes inperfect crystals, because intersections of misfit disloca-tions act as preferred sites for nucleating an interface

dislocation loop [27,28,53,54,57]. As a consequence, theinterface will shear in response to the stress fields ofa nearby lattice dislocation and attract the dislocationinto the interface [27,28,112]. After the incoming dis-location becomes absorbed and extends its core withinthe interface plane, in order for it to transmit into theother crystal, it must then ‘re-nucleate’ and bow-out ontothe outgoing slip system, an event that is aided by ther-mal activation [28,111]. Using atomistic simulations, ithas been demonstrated that a dislocation, nomatter whattype or sign, spontaneously enters the interface, due tothe shear of the interface. The core of the lattice glide dis-location readily spreads within the interface, resulting ina nonplanar core structure. The width of core spreadingincreases with decreasing interface shear strength [27].Thus, core spreading effectively pins a glide dislocationin the interface plane and so ‘weak shear’ interface can bea very strong barrier to slip transmission across interfaces(Figure 5(d)). Atomistic simulations [111] demonstratedthat the weaker the interface, the larger the magnitudeof core spreading, and hence stronger resistance to sliptransmission, as shown in Figure 6.

The ability of an interface to transmit dislocationsmaychange with strain. Over the duration of plastic defor-mation, the interface must interact with a high flux ofdislocations. These dislocations either become stored in

MATER. RES. LETT. 7

Figure 6. Themaximum resolved shear stress required to accom-plish the slip transmission as a function of interface shear strength[111].

the interface or transmit across it. Even if they wereto transmit, residual dislocations are deposited in theinterface since the Burgers vectors of the incoming andoutgoing dislocations are unequal. Thus either way, dis-location–interface interactions can increase the extrinsicdislocation density stored in the interface with appliedstrain. In the event that this extrinsic density is notrecovered, it can affect the ability of the interface totransmit subsequent dislocations. It can be envisionedthat this density could, on the one hand, repel subse-quent dislocations, thereby hindering transmission, or,on the other hand, it can increase the interfacial shearstrength, thereby promoting transmission with strain[27,59,111,112].

3. Plasticity in interfaces

Plastic deformation in nanolaminated materials involvesplasticity in the interface as well as the constituent layers.Interface plasticity is accomplished through nucleation,glide, and climb of dislocations that lie in the interfaceplane. Thus, it is controlled by the interface structuresand properties.

3.1. Glide of interface dislocations

Interface shear occurs via nucleation and glide of inter-face dislocations under effective shear stresses paral-lel to the interface plane [54]. In addition to interfacesliding under applied shear stress, interface shear canbe triggered by the creation of interface dislocationsunder the stress field associated with lattice glide dis-locations impinging on the interface [27,56,82,113,114].The created interface dislocations further attract latticedislocation into the interface. The in-plane component

of Burgers vector of the lattice dislocation then spreadsalong the interface (corresponding to the core spreading),causing interface shear. A glide dislocation blocked by theinterface can also cross-slip into the interface plane with-out core spreading, especially if the interface plane is alsoa glide plane, resulting in interface sliding [27,82,112].

3.2. Climb of interface dislocations

Interface dislocations can climb along the interface planebecause of the low formation energy and low migrationenergy of point defects in interface [53,59,69,115–127], asdemonstrated by molecular dynamics (MD) simulations[116–127]. In particular for a semi-coherent interface,point defects have lower formation energy and lowermigration energy along misfit dislocation lines and atintersections of misfit dislocations [59,124–127]. Thus,an interface has higher equilibrium concentration forpoint defects. Dislocation climb at the Cu–Nb interfacehas been inferred from atomistic simulations (Figure7(a)) [123] and experimentally observed in Al–Nb inter-faces (Figure 7(b1–b3)) [115]. This is consistent witha high vacancy concentration and a high diffusivity ofvacancies in these interfaces. AtomisticMonte Carlo sim-ulations indicate that the Cu–Nb interface can have ahigh vacancy concentration of 0.05 (Figure 7c), about 14orders of magnitude higher than the vacancy concen-tration in the bulk Cu crystal [58]. The mean extendedvacancy formation Ef with respect to the removal ofatoms in the interfacial Cu layer is computed to be0.12 eV/atom. This formation energy is one order ofmag-nitude smaller than the formation energies of vacancies(1.26 eV) or interstitials (3.24 eV) in bulk Cu. In addi-tion, the migration of a point defect in the interfacialplane involves the rearrangement of a group of atomswith an associated delocalized displacement field withinthe interface, unlike single-atom jumps for a vacancy ina bulk crystal. Using the Nudged Elastic Band method,the kinetic barriers associated with the migration fromone delocalized displacement field to the otherwere com-puted in the range of 0.03–0.10 eV by molecular stat-ics simulations. This small kinetic barrier is comparablewith a Cu adatom diffusing on a flat Cu (111) surface[128–131], and results in the high diffusivity of vacancieswithin interfaces. Similar results have been observed inCu–Ni and Cu–Ag interfaces [59].

Because of the easy glide and efficient climb, interfa-cial dislocations canmove within the interface, react withother interfacial dislocations, and interact with pointdefects in the interface. First, the easy glide and effi-cient climb enable slip transmission: glide dislocationscan reassemble the spread cores in the interface planevia climb, and dislocation debris scattered in interfaces

8 J. WANG ET AL.

Figure 7. (a) Molecular dynamics simulations demonstrated dislocation climb along the Cu–Nb interface [123], and (b1–b3) in situ TEMobservations of dislocation climb along the Al–Nb interface [115]. Climb of the out-of-plane component of interfacial dislocations isascribed to (c) a high equilibrium vacancy concentration of 5.8% at 300 K and a low kinetic barrier of 0.03–0.10 eV for vacancy migrationin the interface [55,128].

can reassemble into lattice glide dislocations, facilitatingslip transmission. Second, reactions between interfacialdislocations assisted by glide and climb could lead tothe annihilation of dislocation content (recovery) (Figure7(b)). Third, discrete pile-ups can be absorbed in theinterface plane, assisted by glide and climb in the inter-face, thereby blunting the stress concentration of thepile-up [28,122]. Finally, dislocation climb enables theinterfacial plane to be in an equilibrium state with respectto concentrations of point defects because of absorptionand/or emission of vacancies at dislocation cores. Thus,semi-coherent interfaces offer an ideal platform for thedynamic recovery and reassembly of interface defects.Nanolaminated materials could persist in a damage-freesteady state even when driven far from equilibrium byintense particle radiation [5,26,28,55,122].

3.3. Effect of interface dislocations on strainhardening inmetallic nanolaminates

When the incompatibility of plastic deformation inthe adjacent layers is small, strain hardening is mainlyascribed to the character of accumulated interface

dislocations and interface mechanical properties. Forexample, nanotwinned face centered cubic (fcc) metalsshow a high strain hardening rate than Cu–Nb multi-layers (Figure 8(a)). This is ascribed to the high densityof accumulated interface dislocations in twin bound-aries that originate from the crystallography of slipin the layered microstructure (Figure 8(b)), but theless accumulated dislocations in the Cu–Nb interfacebecause of the dynamic recovery of dislocations assistedby the efficient climb and glide in the Cu–Nb inter-face [58,115,123,132]. By fitting experimentally mea-sured stress–strain curves in the function form of σ

= K1 +K2εn, the coefficientK2 represents the increment

in flow strength due to unit increase in strain. For nt Cu,K1 = 760MPa, K2 = 580MPa, and n = 0.12 [103]. Forcomparison, the values of fitting constants to work hard-ening results in rolled bulk Cu and 2.5 nm Cuss/2.5 nmNb multilayers [133] are K1 = ∼0MPa, K2 = 350MPaand n = 0.35 and K1 = 2250MPa, K2 = 100MPa, andn = 0.05, respectively. The value of K1 is significantlyhigher in nanotwinned Cu than that of bulk Cu as a resultof higher flow strength of the nt Cu, and is lower thanthat of the 2.5 nm Cu/2.5 nm Nb multilayer. The strain

MATER. RES. LETT. 9

Figure 8. (a) Measured true stress—strain curve of nanotwinned Cu foils. (b) Cross-sectional TEMmicrographs of nanotwinned Cu filmsafter 50% thickness reduction, showing a high density of dislocations along twin boundaries without dislocation cell walls in layers[103]. (c) The crystallography of slips in nanotwinned multilayers shows three paired {111} slip systems across the twin interface. (d)Lomer dislocations at the twin interface as a reaction result of the deposited interface dislocations. (e) The crystallography of slips in theKS fcc–bcc system shows three paired {111} slip systems across the interface. (f ) A small residual dislocation results from the reaction ofthe deposited interface dislocations.

hardening rates are calculated to be 10GPa for bulk Cu,0.9GPa for nt Cu, and 0.09GPa for 2.5 nm CuNb multi-layers at the strain level of ∼5%. It is also noticed that ahigher strain hardening rate was measured experimen-tally, 7 GPa in 30 nm Cu/30 nm Nb multilayers at thestrain of ∼5%, but the flow strength is lower than the2.5 nm Cu/Nb multilayers [103].

The difference in strain hardening rate between nan-otwinned Cu and CuNb multilayers is ascribed to thecharacter of accumulated interface dislocations. Thepresence of twin interfaces causes the change in crystalorientations betweenmatrix and twinned crystals, result-ing in the discontinuity of slip systems across twin inter-faces (Figure 8(c)). When nanotwinned Cu is subjected

to normal loading (perpendicular to the twin interfaceplane), lattice dislocations meet at the interface and reactto form Lomer dislocations that cannot glide along theinterface (Figure 8(d)). In addition, shear stresses paral-lel to twin interfaces are minimal, or locally exist in someregions of twin interfaces due to the residual dislocationsat twin interfaces. Therefore, these interface dislocationsare likely to be sessile at twin interfaces, acting as storeddislocations which cause strain hardening. Unlike thetwin interface, slip systems in CuNb multilayers can bepaired to reduce the content of interface dislocations, asshown in Figure 8(e) and (f). In particular, the low for-mation energy of point defects in the CuNb interfaceenables the dislocation climb along the interface [58] and

10 J. WANG ET AL.

Figure 9. (a) High-resolution transmission electron microscope (HRTEM) image of a typical cube-on-cube Cu–Ag interface and (b) finetwin bands in the cube-on-cube Cu–Ag composite. (c) HRTEM image of a typical hetero-twin Cu–Ag interface and (d) a shear band in thehetero-twin Cu–Ag composite. Three paired slip systems form the threefold crystallographic symmetry of slip systems about the normalof the interface [65].

the low interface shear [27,82] facilitates glide of inter-face dislocations that facilitates the recovery of storeddislocation content. Using Synchrotron X-ray micro-diffraction, it was demonstrated that the content of inter-face dislocations does not increase significantly in CuNbnanolayers during straining up to a final cumulativestrain of 35% [132]. Thus, a relatively lower strain hard-ening rate was observed in CuNb multilayers.

3.4. Twin, slip, and shear banding in crystallinelaminates

To demonstrate the correlation of the occurrence of plas-tic flow instability with the crystallography of slip systemsand interface properties, two material systems Cu–Agand Cu–Nb are compared.

Lamellar eutectic Cu–Ag, fabricated via a flux-meltingtechnique, [18, 65, 134, 135] exhibits two kinds of crystal-lographic relations, cube-on-cube and hetero-twin. Bothshare a semi-coherent {111}Cu||{111}Ag interface. Ananalysis of the crystallography of slip systems indicatesthree pairs of slip systems that share the same slip traceon the interface (Figure 9(a) and (b)). The cube-on-cube orientation relationship retains the continuity ofslip across the interface, while the hetero-twin orienta-tion relationship results in the discontinuity of slip acrossthe twin interface (Figure 9(b), also see Figure 8(d)). Asa consequence, the paired slip systems across the inter-face will annihilate the common Burgers vectors in the

cube-on-cube Cu–Ag interface. A very small residualBurgers vector (0.034 nm, approximately 1/10th of thefull Burgers vector) is left on the interface. However,the paired slip systems in the hetero-twin Cu–Ag onlyannihilate the in-plane components, and a large resid-ual Burgers vector (0.221 nm, 86% of full Burgers vector)is left on the interface as a Lomer sessile dislocation(Figure 8(d)).

It is noticed that three paired {111} slip systems holda threefold symmetry around the normal of the interfacein both cube-on-cube and hetero-twin orientation rela-tionships (Figure 9(a) and (c)). When the materials aresubjected to the loading (perpendicular to the interfaceplane), the Schmid factor is 0.32 for all glide dislocationson {111}-type glide planes [65]. Therefore, the activityof dislocations is assumed to be the same on all {111}-type planes. If the same number of slip systems and thesame slip activity on all glide planes are activated in bothCu and Ag, plastic deformation can take place in a sym-metrical mode in both crystals across the interface. Asa result, there is no net rotation of the (111) interface,although the residual dislocations are accumulated on theinterface. However, the activation of dislocations in Agis easier than Cu and twinning commonly occurs in Ag.This causes the development of stress concentrators alongthe interface. With continuous straining, twins in Ag lay-ers transmit into Cu layers in the cube-on-cube Cu–Aglaminates. Once one twinning system is predominated,the other two twinning systems will be either completely

MATER. RES. LETT. 11

suppressed or have lower activity, and plastic flow insta-bility occurs accompanied by the propagation of twinbands across multiple layers. Within this cross-interfacetwin band, the pair of twinning systems on either side ofthe interfaces is well-aligned and the cube-on-cube ori-entation relation is maintained within the band[65]. Thislocalized twin band may be classified as crystallographic(Figure 9(b)).

Differing from the cube-on-cube Cu–Ag laminates,the residual dislocations resulting from paired {111} slipsystems across the twin boundary are Lomer disloca-tions that have Burgers vector perpendicular to the twininterface in the hetero-twin Cu–Ag laminates (also seeFigure 8(d)). In the absence of a symmetrical activationof three sets of paired slip systems, the accumulationof Lomer dislocations causes interface tilting, facilitatingcross-slip of dislocations on the twin interface. This localchange in slip activity could favor large crystallographicrotations and lead to shear banding (Figure 9(d)) in the

hetero-twin Cu–Ag system [65]. In the central core zoneof the shear band, the layered morphology is preserved,the layer thickness has become finer, and the layers haverotated relative to those in the matrix. The shear bandstructure is not aligned with any crystallographic plane,indicating non-crystallographic banding [65,134].

Similar phenomena have also been observed inCu–Nb laminates. Cu–Nb thin films produced by PVD[20,65,136] possess planar Cu–Nb interfaces with a KSorientation relationship (Figure 10(a)). Usingmicropillarcompression, non-crystallographic shear banding occursand runs across the pillar wherein the layers had rotatedto an orientation favorable for interfacial sliding (Figure10(b)) [20,65,136]. The KS orientation relationship ispreserved, but altogether the Cu and Nb crystallographicorientations have reoriented by 28.5°, while the mor-phology of the Cu–Nb interface has only rotated 17.5°.The difference signifies that the crystallographic interfaceplanes have tilted 11° and no longer correspond to the

Figure 10. (a) HRTEM image of a typical KS Cu{111}–Nb{110} interface and (b) a shear band in the composite [65]. (c) HRTEM image ofa typical KS Cu{112}–Nb{112} interface and (d) a shear band in the composite. The white lines in (a) and green lines in (c) indicate thefavorably paired slip systems. (e) and (f ) TEM images of (d), showing fine twins and stacking faults in the Cu layer that are parallel to thefavorably paired slip plane.

12 J. WANG ET AL.

{111}Cu||{110}Nb planes [65,136]. Thus, like the hetero-twin Cu–Ag interface, a shear band is associated withan interface that is resistant to dislocation transmission.It is noticed that an approximate threefold symmetryof paired slip systems is preserved in the KS orienta-tion relationship (also see Figure 8(e)). The instabilityof plastic flow is ascribed to the easy shear interface[27,28,50,54,57,82,111] and the interface tilting whichis triggered by the accumulated residual defects associ-ated with the difference in slip vectors [65]. It is worthpointing out that the local stress state may change thedeformation mode, although the approximate threefoldsymmetry of paired slip systems is preserved. Using thenanoindentation technique, the local shear stress favorsone paired slip system than other two pairs; as a con-sequence, twinning is activated in the Cu layer by sliptransmission from the Nb layer [136]. Under shock load-ing, Han et al. observed many twins in Cu layers due tothe heterogeneous stresses [137].

Cu–Nbnanolaminates fabricated byARB [15,21,23,25],however, contain crystallographically different interfacesthat are more resistant to interface sliding [138,139]and preserve favorable paired slip systems (Figure 10c).Interestingly comparing the electron diffraction patternswithin the as-prepared material and the band in thedeformed material, it is found that the crystals have notrotated with the band [65]. Within the band, the orienta-tions of the (111)Cu and (101̄)Nb planes θ cu and θNb withrespect to the fixed x-axis are distributed within (18–27°)and (23–38°), respectively (Figure 10(d)). These rangesare very similar to those found in the as-prepared mate-rial, that is, (16–24°) and (24–35°). The misorientationacross the interface is also preserved. Further, the bandangle β of ∼25° lies within the ranges of θCu and θNbfor the pair of (111)Cu-(101̄)Nb slip planes, the most well-aligned for slip transmission across the interface (Figure10(c) and (f)). In particular, fine twin bands and highdensity of stacking faults were observed in the Cu lay-ers (Figure 10(e)). Taken together, the above findingssuggest that this plastic instability occurred via succes-sive dislocation transmission across the interfaces on thewell-aligned (111)Cu-(101̄)Nb slip planes, leading to theformation of a slip band.

In summary, the transmissibility of the interface andinterface shear resistance profoundly change the mode ofstrain localization. When the interface permits the trans-mission of slip or twin, crystallographic slip or twin bandsoccur. However, if the interface blocks impinging dislo-cations from transmitting, the accumulation of extrin-sic interface dislocations causes interface plane rotation.The tilt can promote dislocation cross-slip on the inter-face and interface sliding, which are believed to lead tonon-crystallographic shear banding.

3.5. Shear banding in crystal-amorphous laminates

Metal/amorphous laminated composites have been fabri-cated in pursuit of enhanced mechanical and functionalproperties of amorphous layers in the recent years[84–90,97–100,140–153]. The amorphous layer involvesmetallic glasses [84–90,97–100,140–145], amorphousceramics [146–151], and carbon or silicon family elemen-tal glasses [152–157]. To conquermechanical instabilitiesof amorphous materials, the laminated microstructureconstrains the formation and propagation of damage(cracks and shear bands) in amorphous layers andpossibly enables the plastic co-deformation betweenamorphous and metallic layers. The study of mechanicaldeformation of metal/amorphous laminated compositeshas been largely focused on the metal-metallic glass andmetal–amorphous ceramic laminates [84–90,97–100,140–155]. Plastic deformation inmetal–amorphous lam-inates, unlike crystalline laminates, is mainly accom-modated by plastic deformation in metallic layers.The mechanical behavior of amorphous materials isdependent on their category. Amorphous metals (ormetallic glasses) lack strain hardening ability, result-ing in limited elongation after the elastic–strain region[85–90,140–145]. Beyond the elastic limit, metallicglasses deform via STZs and fail by localized shear bands[140–145].

Amorphous ceramics behave very similarly to crys-talline ceramics at room temperature which fails by brit-tle fracture [150,151]. An experimental study of an Al-amorphous SiC system [150] revealed the mechanicalinstability associated with the fracturing of the SiC lay-ers in the nanolaminate at large deformations [151],although nanoscale amorphous SiC layers demonstratedremarkable elastic bending flexibility. The interfacebonding strength of the Al-amorphous SiC was found tobe higher than the rupture strength of pureAl. This is evi-dent as cracks initiate inside Al layers instead at the inter-face [151]. Plastic co-deformation between the Al andamorphous SiC layers could not be achieved [150, 151].

Unlike metal–amorphous ceramics laminates, plas-tic co-deformation has been observed in metal-metallicglass when the thickness of the layers is carefully tuned[84–90,97–100,141–145]. Taking Cu/CuZr glasses as aprototype material, their laminated films were depositedwith alternating layers of amorphous CuZr and crys-talline Cu layers [141–145]. Cui et al. performed a seriesof experimental study [141] in which Cu layers had athickness of 18 nm in all multilayers, and CuZr layershad different thicknesses of 4, 10, 20, 40, 75, and 100 nm,respectively. Scanning electron microscope images of thelaminates after the indentation testing revealed the for-mation of shear bands as theCuZr layer thickness exceeds

MATER. RES. LETT. 13

Figure 11. TEM images of the 40 nm CuZr/Cu multilayer after indentation testing. (a) Six shear bands outlined in the yellow rectanglesand (b) the shear bands SB1 and SB2 end at the CuZr–Cu interfaces. (c) and (d) slip bands in the Cu layers that formed associated withshear on {111} planes nonparallel to the layers. The thin red line in (c) and (d) represents {111} planes in the Cu. Two tilt grain boundaries,GB1 and GB2, are marked in (c), indicating that shear also occurs on the {111} plane parallel to the layers. The regions outlined by theyellow circles show a crystalline structure in the CuZr.

20 nm, while a homogenous plastic deformation in the4 nm CuZr—18 nm Cu and the 10 nm CuZr—18 nm Cumultilayers [141]. Figure 11 shows the cross-sectionaltransmission electron microscope images of the 40 nmCuZr—18 nm Cu multilayer. In Figure 11(a), we markedsix shear bands in the rectangles, SB1 to SB6. Fourintriguing features are characterized. (1) Shear bands didnot nucleate from surfaces of the samples; (2) shear bandscut through several crystalline and amorphous layers; (3)localized shear in the Cu layers is accomplished via slipon {111} planes; and (4) shear bands are approximatelyparallel to the {111} plane in the Cu layers (nonparallelto interface plane). In this scenario, slip bands are trig-gered in theCu layers to accommodate the localized sheardeformation associated with the extension of shear bandsin the CuZr layers, as observed in Figure 11(c) and (d),and schematically illustrated in Figure 12.

The lack of shear banding in the 4 nm and 10 nmCuZr/Cu multilayers could be understood according to

plastic co-deformation mechanisms. Noted that thereexists a critical length scale of 10–20 nm for amor-phous CuZr alloys, below which amorphous CuZrlayers can plastically deform via the so-called STZs[84–90,97–100,141–145]. The deposited dislocations atinterfaces act as stress concentrators, facilitating the for-mation of STZs at interfaces in CuZr layers and achievingplastic deformation transmission from the Cu layer tothe CuZr layer, as illustrated in Figure 12(a) and demon-strated by MD simulations [90,141].

With the increase in the CuZr layer thickness, the ten-sile stress in the CuZr layers and the interaction forcebetween the deposited dislocations at the adjacent inter-faces decrease. Even though STZs are formed at inter-faces, the propagation of the STZs across the entireCuZr layer is slowed down due to the reduced shearstress on the plane nonparallel to the CuZr layers. Whenincreasing the applied compressive stress, the resultantshear stress on the plane nonparallel to the CuZrlayers

14 J. WANG ET AL.

Figure 12. Schematics of plastic deformationmodes with respect to the CuZr layer thickness. (a) Plastic co-deformation in the thin CuZrlayers, showing plastic deformation in the Cu layers via slip on {111} planes and the formation and reaction of STZs in the CuZr layers.The red ellipses represent STZs. (b) The formation and propagation of shear bands in the thick CuZr layers, showing propagation of shearbands into the Cu layers, are accomplished via the formation of slip bands on {111} planes. The dashed lines represent {111} planesnonparallel to the layers.

eventually triggers the formation of shear bands by gath-ering STZs in the CuZr layers. The formed shear bandsthen propagate toward the adjacent interfaces, and con-sequently trigger plastic deformation in the Cu layers.Corresponding to the crystallography of the Cu layer, slipon {111} planes via either Shockley partial dislocations orfull dislocations accommodate the localized shear defor-mation in the adjacent CuZr layers. As a consequence,slip bands are formed in theCu layers parallel to the {111}planes, constraining shear bands in the CuZr layers thatare parallel to the {111} plane in the Cu layers. Accom-panying the propagation of such shear bands, the shearstress in the front of the shear bands decreases, associatedwith the development of a zone of plastic deformation,and the shear bands are more likely to eventually stoppropagation at the CuZr–Cu interfaces.

4. Summary

Due to a high density of interfaces, geometrical con-straints from layered geometry, controllable layer thick-ness, designed interfaces (orientation relationship, atomicstructure, and interface shear strength), and nanolam-inated composites achieve a unique combination ofmechanical properties—high flow strength, good duc-tility, thermal stability, and plastic flow stability atlarge strains. In particular, the mechanical behavior of

nanolaminates is dominated by interfaces that act assources, barriers, and preferred sites for storage anddynamic recovery of glide dislocations.

Theory andmodeling at different length scales includ-ing atomistic [27–29,56,72–74,90,91,158], discrete dis-location dynamics [159–168], and crystal plasticity[169,170], integrated with experimental observations,provide insights into understanding the interface-dominated behavior of nanolaminates. However, incor-porating all of the relevant interface physics into themultiscale models to develop predictive capability is stilla challenge [53,114].

Acknowledgements

JW and AM acknowledge research sponsorship by DOE,Office of Basic Energy sciences. SS acknowledges the start-upgrant provided by the Louisiana State University. The authorsacknowledge collaborations with J.P. Hirth, R.G. Hoagland,N.A. Mara, I.J. Beyerlein, N. Li at Los Alamos National Lab-oratory, H.J. Chu at Shanghai University, K. Kang at YonseiUniversity, S.J. Zheng at Shenyang National Laboratory forMaterials, R.F. Zhang at Beihang University, and C.Z. Zhu atMissouri University of Science and Technology.

Disclosure statement

No potential conflict of interest was reported by theauthors.

MATER. RES. LETT. 15

ORCiD

Jian Wang http://orcid.org/0000-0001-5130-300X

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